cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A321761 Irregular triangle read by rows where T(H(u),H(v)) is the coefficient of m(v) in s(u), where H is Heinz number, m is monomial symmetric functions, and s is Schur functions.

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%I A321761 #4 Nov 20 2018 19:45:53
%S A321761 1,1,1,1,0,1,1,1,1,0,1,2,1,1,1,1,1,0,0,1,0,1,0,1,2,0,1,1,2,3,1,1,1,1,
%T A321761 1,1,1,0,0,0,1,3,1,1,1,1,1,1,1,1,1,1,1,0,1,1,2,2,3,4,0,0,1,2,1,3,5,0,
%U A321761 0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
%N A321761 Irregular triangle read by rows where T(H(u),H(v)) is the coefficient of m(v) in s(u), where H is Heinz number, m is monomial symmetric functions, and s is Schur functions.
%C A321761 Row n has length A000041(A056239(n)).
%C A321761 The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%H A321761 Wikipedia, <a href="https://en.wikipedia.org/wiki/Symmetric_polynomial">Symmetric polynomial</a>
%F A321761 If s(y) = Sum_{|z| = |y|} c(y,z) * m(z), then Sum_{|z| = |y|} c(y,z) * P(z) = A296188(H(y)), where P(y) is the number of distinct permutations of y.
%e A321761 Triangle begins:
%e A321761    1
%e A321761    1
%e A321761    1   1
%e A321761    0   1
%e A321761    1   1   1
%e A321761    0   1   2
%e A321761    1   1   1   1   1
%e A321761    0   0   1
%e A321761    0   1   0   1   2
%e A321761    0   1   1   2   3
%e A321761    1   1   1   1   1   1   1
%e A321761    0   0   0   1   3
%e A321761    1   1   1   1   1   1   1   1   1   1   1
%e A321761    0   1   1   2   2   3   4
%e A321761    0   0   1   2   1   3   5
%e A321761    0   0   0   0   1
%e A321761    1   1   1   1   1   1   1   1   1   1   1   1   1   1   1
%e A321761    0   0   0   1   0   2   5
%e A321761 For example, row 15 gives: s(32) = m(32) + 2m(221) + m(311) + 3m(2111) + 5m(11111).
%Y A321761 Row sums are A321762.
%Y A321761 Cf. A000085, A008480, A056239, A082733, A124795, A153452, A296188, A300121, A321742-A321765.
%K A321761 nonn,tabf
%O A321761 1,12
%A A321761 _Gus Wiseman_, Nov 20 2018